All 34 members of the Congress Working Committee, the party's highest decision-making body, could quit in a gesture of “collective responsibility.”
NDTV reported on Sunday quoting unnamed party sources.
The top leaders of the Congress party will meet Monday evening to try and make sense of the party's worst performance ever, the report said.
There are reports that the Gandhis will offer to step down when the Congress Working Committee meets this evening - however their resignation would almost certainly be rejected by colleagues.
Their colleagues have made it clear that while a detailed post-mortem will be conducted, the First Family will be shielded from direct blame, NDTV quotes party insiders.
Kamal Nath, the most senior Congress parliamentarian, told NDTV on Sunday that only internal democracy could end “the culture of patronage.” He added: “Why blame Rahul alone? He should not resign.”
The Congress slumped to its worst-ever defeat last week, claiming just 44 seats in the 543-member parliament, as the opposition BJP and its prime ministerial candidate, Narendra Modi, swept to power with the first majority in 30 years.
Accepting responsibility of the defeat on Friday, Rahul said the Congress was doing “pretty badly.”
Sonia Gandhi, the 67-year-old Congress party president, entrusted campaigning to her son, whose lacklustre performance failed to convince voters as Congress sought a third term in power.
Its defeat has been attributed to a sharp economic slowdown, rising food prices and a slew of corruption scandals, as well as Rahul Gandhi, 43, being comprehensively overshadowed by BJP leader Narendra Modi.
The BJP leader assailed the dynastic rule of the Gandhis and tapped into widespread hunger for jobs and development, while offering a message of aspiration and ambition to the young electorate.